Question: Simplify; express your answer in exponential form. Assume $z\neq 0, x\neq 0$. $\dfrac{{(z^{-4})^{-1}}}{{(z^{3}x^{5})^{2}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${z^{-4}}$ to the exponent ${-1}$ . Now ${-4 \times -1 = 4}$ , so ${(z^{-4})^{-1} = z^{4}}$ In the denominator, we can use the distributive property of exponents. ${(z^{3}x^{5})^{2} = (z^{3})^{2}(x^{5})^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(z^{-4})^{-1}}}{{(z^{3}x^{5})^{2}}} = \dfrac{{z^{4}}}{{z^{6}x^{10}}}$ Break up the equation by variable and simplify. $\dfrac{{z^{4}}}{{z^{6}x^{10}}} = \dfrac{{z^{4}}}{{z^{6}}} \cdot \dfrac{{1}}{{x^{10}}} = z^{{4} - {6}} \cdot x^{- {10}} = z^{-2}x^{-10}$.